Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
920 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21434645 | C2 | semidirect |
| 5. #21425077 | C2 | semidirect |
| 6. #21424941 | C2 | semidirect |
| 7. #21424310 | C2 | semidirect |
| 9. C59×#2642 | C2 | semidirect |
| 188. #2642 | D59 | semidirect |
| 225. C59 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437980 | 2 |
| #21434645 | 2 |
| #21433914 | 2 |
| #21425313 | 2 |
| #21425077 | 2 |
| #21424941 | 2 |
| #21424310 | 2 |
| #21423907 | 2 |
| C59×#2642 | 2 |
| #25691 | 59 |